Magnetic resonance imaging (MRI) is a medical imaging technique in widespread use for viewing the structure and function of the human body. MRI systems provide soft-tissue contrast, such as for diagnosing many soft-tissue disorders. MRI systems generally implement a two-phase method. The first phase is the excitation phase, in which a magnetic resonance signal is created in the subject. To that end, the body being examined is subjected to a main magnetic field, B0, to align the individual magnetic moments, or spins, of the nuclei in the tissue with the axis of the polarizing field (conventionally, the z-axis). The main magnetic field also causes the magnetic moments to resonantly precess about the axis at their characteristic Larmor frequency. If the tissue is then subjected to a radio frequency (RF) excitation pulse, B1, with a frequency near the Larmor frequency, a magnetic field in the x-y plane re-orients, flips, or tips the net aligned moment, Mz, into or toward the x-y plane, producing a net transverse magnetic moment Mxy, the so-called spin magnetization. The second phase is the acquisition phase, in which the system receives an electromagnetic signal emitted as the excited nuclei relax back into alignment with the z-axis after the excitation pulse B1 is terminated. These two phases are repeated pair-wise to acquire enough data to construct an image.
The excitation phase is generally tailored to localize the excitation pulse to a specific region within the subject, such as a 3D slab or a relatively thin 2D slice. The subsequent acquisition phase encodes the localized region in all three dimensions for a 3D slab or only in-plane for a thin slice. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which magnetic field gradients (Gx, Gy, and Gz) vary according to the particular localization method being used. Tailored RF pulses are also used to localize the excitations. Scan sequences containing these RF pulses and gradients are stored in a library accessed by commercial MRI scanners operating at a main magnetic field strength of 1.5 Tesla or lower to meet the needs of many different clinical applications.
The MR signals acquired with an MRI system are signal samples of the subject of the examination in Fourier space, or what is often referred to in the art as “k-space.” Each MR measurement cycle, or pulse sequence, typically samples a portion of k-space along a sampling trajectory characteristic of that pulse sequence. Most pulse sequences sample k-space in a raster scan-like pattern sometimes referred to as a “spin-warp”, a “Fourier”, a “rectilinear”, or a “Cartesian” scan. The spin-warp scan technique employs a variable amplitude phase encoding magnetic field gradient pulse prior to the acquisition of MR spin-echo signals to phase encode spatial information in the direction of this gradient. In a two-dimensional implementation (“2DFT”), for example, spatial information is encoded in one direction by applying a phase encoding gradient, Gy, along that direction, and then a spin-echo signal is acquired in the presence of a readout magnetic field gradient, Gx, in a direction orthogonal to the phase encoding direction. The readout gradient present during the spin-echo acquisition encodes spatial information in the orthogonal direction. In a typical 2DFT pulse sequence, the magnitude of the phase encoding gradient pulse, Gy, is incremented, ΔGy, in the sequence of measurement cycles, or “views” that are acquired during the scan to produce a set of k-space MR data from which an entire image can be reconstructed.
Most MRI scanners use a single-channel RF excitation coil to tip the spin magnetization away from its equilibrium state and initiate a measurement cycle. Usually, a radio frequency (“RF”) excitation pulse is used to excite either all of the spins inside the excitation coil (non-selective excitation), a single slice through the subject (slice-selective excitation), or within only a specific region, such as, a small cube (3-D spatially-selective excitation). In spatially-selective, spatially-tailored excitation, the RF pulse is transmitted in the presence of gradient waveforms that impart a time-varying gradient onto the main magnetic field of the MRI system, which is instrumental in the spatial and selective excitation process. In general, the gradient field may be viewed as causing the traversal of a curve in excitation k-space, a path that may proceed through all three dimensions of k-space (kx, ky, and kz), which under certain assumptions is essentially a 3-D Fourier domain. During this traversal of excitation k-space, the energy of the RF pulse being played in conjunction with the gradient waveforms may be viewed as depositing RF energy along this k-space excitation trajectory curve. The RF pulse thus produces an excitation that modulates (in phase, in amplitude, or both) as a function of position (kx, ky, and kz) in excitation k-space. The resulting excitation is often closely related to the inverse Fourier transform of this deposited energy.
For example, in a typical slice-selective RF pulse, a constant gradient field is applied in the z-direction while an RF pulse shaped like a sine cardinal (“sinc”) function is transmitted through the MRI system's single excitation coil. In this instance, the gradient field causes the RF pulse energy to be deposited along a single line (a “spoke”) in the kz-direction of excitation k-space, that is, a line through the k-space position (0,0,kz). This sine-like deposition in kz excites only those magnetic spins within a thin slice of tissue due to the Fourier relationship between energy deposited in excitation k-space and the flip angle of the resulting magnetization. In short, the magnetization that results from this typical RF pulse is a constant degree of excitation within the slice and no excitation out of the slice.
Higher magnetic field strength scanners have been recently used to improve image signal-to-noise ratio and contrast. However, a spatial variation in the magnitude of the RF excitation magnetic field, B1+, occurs with main magnetic field strengths of, for example, 7 Tesla. This undesirable non-uniformity in the excitation across the region of interest is commonly referred to as “center brightening,” “B1+ inhomogeneity” or “flip angle inhomogeneity.”
Newer-generation MRI systems have generated RF pulses with a spatially tailored excitation pattern to mitigate B1+ inhomogeneity by exciting a spatial inverse of the inhomogeneity. In these systems, a plurality of individual radio-frequency pulse trains are transmitted in parallel over the different independent radio-frequency transmit channels. Individual RF signals are then applied to the individual transmit channels, e.g., the individual rods of a whole-body antenna. This recent method, referred to as “parallel transmission” or “parallel excitation,” exploits variations among the different spatial profiles of a multi-element RF coil array. Parallel excitation has enabled several important applications beyond the mitigation of B1+ inhomogeneity, including flexibly shaped excitation volumes.
A number of methods have been proposed for the design of the RF and gradient waveforms for parallel excitation, such as those disclosed, for example, by U. Katscher, et al., in “Transmit SENSE,” Magnetic Resonance in Medicine, Vol. 49, p. 144-150 (2003); by Y. Zhu in “Parallel Excitation with an Array of Transmit Coils,” Magnetic Resonance in Medicine, Vol. 51, p. 775-784 (2004); by M. Griswold, et al., in “Autocalibrated Accelerated Parallel Excitation (Transmit-GRAPPA),” Proceedings of the 13th Annual Meeting of ISMRM, p. 2435 (2005); and by W. Grissom, et al., in “Spatial Domain Method for the Design of RF Pulses in Multicoil Parallel Excitation,” Magnetic Resonance in Medicine, Vol. 56, p. 620-629 (2006).
Successful implementations have been demonstrated on multi-channel hardware, including those described by P. Ullmann, et al., in “Experimental Analysis of Parallel Excitation Using Dedicated Coil Setups and Simultaneous RF Transmission on Multiple Channels,” Magnetic Resonance in Medicine, Vol. 54, p. 994-1001 (2005); by D. Xu, et al., in “A Noniterative Method to Design Large-Tip-Angle Multidimensional Spatially-Selective Radio Frequency Pulses for Parallel Transmission,” Magnetic Resonance in Medicine, Vol. 58, p. 326-334 (2007); and by P. Vernickel, et al., in “Eight-Channel Transmit/Receive Body MRI Coil at 3T,” Magnetic Resonance in Medicine, Vol. 58, p. 381-389 (2007).
Spatially-tailored excitations using parallel transmission methods are designed to provide a prescribed excitation pattern at the Larmor frequency of a specific spin species. As such, the parallel transmission of RF excitation pulses in the presence of two-dimensional (2D) and three-dimensional (3D) gradient trajectories offers a flexible means for volume excitation and the mitigation of inhomogeneity in the main magnetic field, B0, and the excitation field, B1+. Parallel transmission systems are adept at these tasks because their RF excitation arrays include multiple independent transmission elements with unique spatial profiles that may be modulated and superimposed to tailor the magnitude and phase of the transverse magnetization across a chosen field-of-excitation (FOX). Parallel transmission systems allow reduction of the duration of an RF pulse by increasing the amplitude and slew rates of the system's gradient coils. Namely, the excitation k-space trajectory may be undersampled (reducing the distance traveled in k-space), in turn shortening the corresponding RF pulse. The ability to “accelerate” in the k-space domain arises due to the extra degrees of freedom provided by the system's multiple transmit elements.
Unfortunately, parallel transmission techniques generally increase peak pulse power, giving rise to concerns regarding excessive exposure to RF energy. In this context, the RF exposure is generally directed to a physiological absorption of the RF irradiation, rather than the transmitted RF energy. A typical measure of the radio-frequency absorption is the specific absorption rate, or SAR, which specifies the deposited power per unit weight (watts/kg) due to the RF pulse. Maximum values for SAR are specified by safety regulations and should be met both globally (e.g., power absorbed by the whole head or whole body) and locally (e.g., power absorbed per 10 grams of tissue). For example, a standardized limit of 4 watts/kg applies to the global SAR of a patient according to an IEC (International Electrotechnical Commission) standard.
When multiple transmit channels are simultaneously employed, the local electric fields generated by each channel undergo local superposition, and local extremes in electric field magnitude may arise, leading to spikes in local SAR. Recent studies have confirmed the presence of “hot spots” and found that parallel transmitted pulses produce relatively high ratios of local to whole-head average SAR, as is described by, for example, F. Seifert et al., in “Patient Safety Concept for Multichannel Transmit Coils,” J Magn. Reson. Imag., 26:1315-1321 (2007). These relatively-high ratios of local to whole-head average SAR make local SAR the limiting factor of parallel transmission MRI. Concerns regarding elevated SAR levels are also set forth in U. Katscher and P. Bornert in “Parallel RF Transmission in MRI.” NMR Biomed, 19:393-400 (2006).
One technique for SAR reduction involves placing constraints on global and local SAR. In this method, SAR constraints are explicitly built into the pulse design process. Because both whole-head mean SAR and local N-gram SAR at any location can be expressed quadratically in terms of pulse sample values, constraints on both whole-head and local SAR can be incorporated simply by adding quadratic constraints to the design method. For example, the method described by I. Graesslin, et al., in “A Minimum SAR RF Pulse Design Approach for Parallel Tx with Local Hot Spot Suppression and Exact Fidelity Constraint,” Proc. Intl. Soc. Magn. Reson. Med., 2008; 612, explicitly accounts for global SAR as well as local SAR at several spatial locations by incorporating several quadratic constraints into the design. However, this approach presents the computationally-intractable problem of solving a system of equations with tens of thousands (or millions) of quadratic constraints.